Abstract
Extreme learning machine (ELM) is a popular randomization-based learning algorithm that provides a fast solution for many regression and classification problems. In this article, we present a method based on ELM for solving the spectral data analysis problem, which essentially is a class of inverse problems. It requires determining the structural parameters of a physical sample from the given spectroscopic curves. We proposed that the unknown target inverse function is approximated by an ELM through adding a linear neuron to correct the localized effect aroused by Gaussian basis functions. Unlike the conventional methods involving intensive numerical computations, under the new conceptual framework, the task of performing spectral data analysis becomes a learning task from data. As spectral data are typical high-dimensional data, the dimensionality reduction technique of principal component analysis (PCA) is applied to reduce the dimension of the dataset to ensure convergence. The proposed conceptual framework is illustrated using a set of simulated Rutherford backscattering spectra. The results have shown the proposed method can achieve prediction inaccuracies of less than 1%, which outperform the predictions from the multi-layer perceptron and numerical-based techniques. The presented method could be implemented as application software for real-time spectral data analysis by integrating it into a spectroscopic data collection system.
Highlights
Spectroscopy is one of the primary exploratory tools that have been used to study the micro-world, investigating the physical structure of substances at the atomic and molecular scale, and characterizing the properties of novel materials, as the physical structure and properties of substances at the micro-world scale cannot be directly measured or observed by any instruments
The problem of spectral data analysis can be defined as an inverse problem, because it gives a set of spectral data or measured spectroscopic curves and requires acquiring the cause—the values of the physical parameters governing the corresponding physical process
As the neural network technique has been successfully applied to resolve many regression and classification problems, we proposed using a special class neural network named extreme learning machine (ELM) to approximate the nonlinear regression function where the spectrum is treated as input via n nodes and the structural parameter p vector is the output, and the built network constitutes a mathematical realization of the multivariate nonlinear regression model f i model (y(E1 ), y(E2 ), . . . , y(En )), i = 1, 2, . . . , n
Summary
Spectroscopy is one of the primary exploratory tools that have been used to study the micro-world, investigating the physical structure of substances at the atomic and molecular scale, and characterizing the properties of novel materials, as the physical structure and properties of substances at the micro-world scale cannot be directly measured or observed by any instruments. MLP model could quantitatively predict the sample structure with reasonable accuracies, provided a sufficient amount of training data These investigations appear to be a great advancement toward developing a relatively easy data-driven analysis approach, without much expert knowledge involved. Four benchmark spectroscopic datasets [22] involving food samples including coffee, olive oil, meat, and fruit, with corresponding measured near-mid infrared spectroscopy were used in their investigations They compared the experimental results from the ELM algorithm with those from other methods like back-propagation artificial neural networks (BP-ANN), Algorithms 2021, 14, 18 k-nearest neighbor (KNN), and support vector machines (SVM). The proposed method is a general-use approach for any spectra-oriented applications It has been demonstrated by a set of RBS data with producing accurate predictions of the physical sample structures.
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